Tom's utility is given by U(X,Y) = 6X^1/4Y^3/4 . Tom has an income of 320 to spend on good X and good Y. Knowing that p_x= 4 and p_y= 8:

a) Calculate the value of utility at the optimal level in a). [Hint: substitute the values of X and Y in U(X,Y) = 6X^1/4Y^3/4 ]

b) Consider now that Tom's preferences change to U (X,Y) =12X^1/2 Y^1/2 while the price of X and Y, as well as income, remain the same as in section a), p_x = 4 and p_y = 8. What is the new optimal bundle of X and Y? Show this graphically (draw a separate graph than a).